Definite Integrals in for-loop

Question

T 2016-9-9

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/302468-definite-integrals-in-for-loop

评论： T 2016-9-22

I'm trying to setup up this loop. But before I do that I need to declare the functions:

n_grid   =    20;  %  Size  of    rid
Ms       =    [];
Js       =    [];
Ns       =    [];
Es       =    [];
J        =    linspace(0,1,1000);
kappa = 2.*sinh(2*J)./(cosh(2*J)).^2;
kappam = 2*(tanh(2*J)).^2-1;
z = exp(-2*J);
K1 = int(sqrt(1- kappam.^2 * sin(phi).^2), phi= 0.. pi/2)
% Calculating Energy & Magnetisation as a function of interaction strength
E = -J.*(coth(2*J)).*(1+(2/pi)*kappam.*K1(kappam));

An error for K1 shows as follows:

Undefined function 'K1' for input arguments of type 'char'.
Error in ising (line 12)
K1 := int(sqrt(1- kappam.^2 * sin(phi).^2), phi= 0.. pi/2)

What's wrong with my syntax?

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Answer 1

Andrei Bobrov 2016-9-9

1
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/302468-definite-integrals-in-for-loop#answer_234267

编辑：Andrei Bobrov 2016-9-9

在 MATLAB Online 中打开

Please try code below

J = linspace(0,1,1000);
kappam = 2*(tanh(2*J)).^2-1;
f = @(phi)sqrt(1- kappam.^2 * sin(phi).^2);
K1 = integral(f,0,pi/2,'ArrayValued',true);

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T 2016-9-13

在 MATLAB Online 中打开

That works:

n_grid   =          20;          %  Size  of    rid
Ms          =          [];
Js          =          [];
Ns          =          [];
Es          =          [];
J          =          linspace(0,1,1000);
kappa          =          2.*sinh(2*J)./(cosh(2*J)).^2;
kappam          =          2*(tanh(2*J)).^2-1;
z          =          exp(-2*J);
f = @(kappa,phi)1./sqrt(1- kappa.^2 * sin(phi).^2);
K1 = @(k)integral(@(phi)f(kappa,phi),0,pi/2,'ArrayValued',true);
%          Calculating          Energy          &          Magnetisation          as          a          function          of          interaction          strength
E          =          -J.*(coth(2*J)).*(1+(2/pi)*kappam.*K1(kappam));
M1          =          ((1+z.^2).^(1/4).*(1-6*z.^2+z.^4).^(1/8))./(1-z.^2).^(1/2);
M2          =          -((1+z.^2).^(1/4).*(1-6*z.^2+z.^4).^(1/8))./(1-z.^2).^(1/2);
M1(1,1:441)          =          0;          %When          J          <          J_c,          M          =          0
M1(1,1:441)          =          0;          %When          J          <          J_c,          M          =          0
for          i          =          1:12000
%while          (1),
%          Choose          a          random          value          between          0          and          1          for          the          interaction          strength
J          =          rand()+1e-10;
%          Perform          a          simulation
[M,          N,          E]          =          ising2(n_grid,          J);
%          Records          the          results
Ms          =          [Ms          M/(n_grid^2)];
Es          =          [Es          E/(n_grid^2)];
Ns          =          [Ns          N];
Js          =          [Js          J];
i          =          i+1;
end

Undefined function 'ising2' for input arguments of type 'double'.

Error in ising (line 27) [M, N, E] = ising2(n_grid, J);

Walter Roberson 2016-9-22

I had no problems with the software once I had done what I indicated above needed to be done.

You might notice that the code in ising.m is spaced oddly. That is because I copied it directly from the pdf and did not bother to change the spacing.

T 2016-9-22